Investigation of optical solitons in a weakly nonlocal Schrödinger equation with parabolic nonlinearity

Hashemi, Mir Sajjad; Mirzazadeh, Mohammad; Ur Rehman, Hamood; Arnous, Ahmed H.; Bayram, Mustafa; Eslami, Mostafa

doi:10.22034/cmde.2024.61598.2673

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	Investigation of optical solitons in a weakly nonlocal Schrödinger equation with parabolic nonlinearity
Computational Methods for Differential Equations
مقاله 23، دوره 14، شماره 3، مهر 2026، صفحه 1375-1386 اصل مقاله (729.23 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61598.2673
نویسندگان
Mir Sajjad Hashemi¹؛ Mohammad Mirzazadeh²؛ Hamood Ur Rehman³؛ Ahmed H. Arnous⁴؛ Mustafa Bayram⁵؛ Mostafa Eslami^* ⁶
¹Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.
²Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran.
³Department of Mathematics, University Of Okara, Okara, Pakistan.
⁴Department of Physics and Engineering Mathematics, Higher Institute of Engineering,El Shorouk Academy-11837, Cairo, Egypt.
⁵Computer Engineering, Biruni University, Istanbul, Turkey.
⁶Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
چکیده
The weakly nonlinear Schr¨odinger equation (NLSE) describes wave phenomena in media characterized by weakly nonlinear dispersion. As a versatile framework, it finds application across diverse fields such as plasma waves, water waves, fiber optics, and Bose-Einstein condensates, and this study focuses on investigating various solutions for the weakly nonlocal NLSE with parabolic law nonlinearity. By employing the Nucci reduction method (NRM), we extract exact solutions, including dark and bright solitons and other traveling wave solutions. This technique is particularly valuable for identifying nonlocal symmetries of differential equations, providing an efficient analytical tool for nonlinear problem-solving in engineering and related domains. Furthermore, we derive a first integral through the reduction method. These results are essential for understanding soliton wave propagation in weakly nonlocal media with parabolic law nonlinearity, providing insights into wave dynamics for the proposed model. Finally, two- and three-dimensional density plots are presented to illustrate the physical behavior of some obtained solutions within the governing model.
کلیدواژه‌ها
Schrödinger model؛ Parabolic law؛ First integral؛ Soliton solution؛ Nucci method

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Investigation of optical solitons in a weakly nonlocal Schrödinger equation with parabolic nonlinearity